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Continuity and Differentiability

Short Answer Type

151. Differentiate the following w.r.t.x:

straight e to the power of straight x cubed end exponent

90 Views

152. Differentiate the following w.r.t.x:

square root of straight e to the power of square root of straight x end exponent end root comma straight X greater than 0

97 Views

153. Differentiate e^x + e^x² +....+ e^x⁵. w.r.t.x.

76 Views

154. Differentiate the following w.r.t.x :log (log x),x>1

94 Views

155. Differentiate the following w.r.t.x :log7 (log x)

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156. Differentiate (3x² - 9 x + 5)⁹ w.r.t.x.

92 Views

157. Differentiate

square root of 15 straight x squared minus straight x plus 1 end root straight w. straight r. straight t space straight x

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158.

Differentiate space square root of 3 straight x plus 2 end root plus fraction numerator 1 over denominator square root of 2 straight x squared plus 4 end root end fraction straight w. straight r. straight t space space straight x.

90 Views

159. Differentiate $square root of fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction end root$ W.r.t x.

Let space straight y equals square root of fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction end root equals open parentheses fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction close parentheses to the power of 1 half end exponent dy over dx equals 1 half open parentheses fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction close parentheses to the power of negative 1 half end exponent straight d over dx open parentheses fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction close parentheses equals 1 half open parentheses fraction numerator straight x plus 1 over denominator straight x minus 1 end fraction close parentheses to the power of 1 half end exponent open square brackets fraction numerator left parenthesis straight x plus 1 right parenthesis begin display style straight d over dx end style left parenthesis straight x minus 1 right parenthesis minus left parenthesis straight x minus 1 right parenthesis begin display style straight d over dx end style left parenthesis straight x plus 1 right parenthesis over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction close square brackets space space space space space space space space equals 1 half open parentheses fraction numerator straight x plus 1 over denominator straight x minus 1 end fraction close parentheses to the power of 1 half end exponent open square brackets fraction numerator left parenthesis straight x plus 1 right parenthesis.1 minus left parenthesis straight x minus 1 right parenthesis.1 over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction close square brackets equals 1 half fraction numerator left parenthesis straight x plus 1 right parenthesis to the power of begin display style 1 half end style end exponent over denominator left parenthesis straight x minus 1 right parenthesis to the power of begin display style 1 half end style end exponent end fraction open square brackets fraction numerator straight x plus 1 minus straight x plus 1 over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction close square brackets space space space space space space space space equals 1 half fraction numerator left parenthesis straight x plus 1 right parenthesis to the power of begin display style 1 half end style end exponent over denominator left parenthesis straight x minus 1 right parenthesis to the power of begin display style 1 half end style end exponent end fraction fraction numerator 2 over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction equals fraction numerator 1 over denominator left parenthesis straight x minus 1 right parenthesis to the power of 1 half end exponent. left parenthesis straight x plus 1 right parenthesis to the power of 3 over 2 end exponent end fraction

84 Views

160. Differentiate the following w.r.t.x:

left parenthesis 4 straight x cubed minus 5 straight x squared plus 1 right parenthesis to the power of 4

91 Views

Previous Year Papers

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Test Yourself

Short Answer Type

159. DifferentiateW.r.t x.

159. Differentiate $square root of fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction end root$ W.r.t x.